The magnitude loss is used to model the HB magnitude. To make the WB enhancement results consistent with the human hearing, we introduce the time-domain SI-SNR to measure the complex spectrum compressed by the auditory loudness power exponent \(\mathbf {\gamma }\)  [1]}. In addition, FocalLoss [2]} is used as a loss function for the SED. The loss function of the whole model is defined as,
\(L = L_\text{HB} + L_\text{APC}^{\mathbf {S}^{\text{WB}^{\prime }}} + L_\text{APC}^{\mathbf {S}^{\text{WB}^{\prime \prime }}} + L_\text{focal}\) 
\(L_\text{HB} = \left\Vert  |\mathbf {S}^{\text{HB}^{\prime }}| - |\dot{\mathbf {S}}^{\text{HB}}| \right\Vert ^2 + \left\Vert \log |\mathbf {S}^{\text{HB}^{\prime }}| - \log |\dot{\mathbf {S}}^{\text{HB}}|\right\Vert ^2\) 
\(L_\text{focal} = -\alpha (1-P_{t,f})^\beta \cdot \log {P_{t,f}}\) 
\(\left\lbrace \begin{array}{ccl}\mathbf {S}^{\text{WB}^{\prime }}_\text{C}&= |\mathbf {S}^{\text{WB}^{\prime }}| \odot (|\mathbf {S}^{\text{WB}^{\prime }}|+1)^{\frac{\mathbf {\gamma }-1}{2}} \odot e^{j\mathbf {S}^{\text{WB}^{\prime }}_{\text{phase}}} \\\dot{\mathbf {S}}^{\text{WB}}_\text{C}&= |\dot{\mathbf {S}}^{\text{WB}}| \odot (|\dot{\mathbf {S}}^{\text{WB}}|+1)^{\frac{\mathbf {\gamma }-1}{2}} \odot e^{j\dot{\mathbf {S}}^{\text{WB}}_{\text{phase}}} \\\mathbf {S}_{\text{t}}&= (<\mathbf {S}^{\text{WB}^{\prime }}_\text{C},\dot{\mathbf {S}}^{\text{WB}}_\text{C}> \cdot \dot{\mathbf {S}}^{\text{WB}}_\text{C})/||\dot{\mathbf {S}}^{\text{WB}}_\text{C}||^2 \\L_\text{APC}^{\mathbf {S}^{\text{WB}^{\prime }}}&=10\log _{10}{\left(||\mathbf {S}_{\text{t}}||^2/||\mathbf {S}^{\text{WB}^{\prime }}_\text{C} -\mathbf {S}_{\text{t}}||^2\right)} \\\end{array} \right.\) 
